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You want to buy a $181,000 home. You plan to pay 15% as a down payment, and take out a 30 year fixed loan for the rest.
Round all answers to the nearest cent as needed.

a) How much is the loan amount going to be?
$


b) What will your monthly payments be if the interest rate is 4.5%?
$


c) What will your monthly payments be if the interest rate is 5.5%?
$
Submit QuestionQuestion 4

Sagot :

Semsee45idn

Answer:

a)  $153,850

b)  $779.54

c)  $873.54

Step-by-step explanation:

Part a)

[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]

Therefore, the loan amount is $153,850.

Part b)

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]

Given:

  • P = $153,850
  • i = 0.045 per year = 0.045/12 per month
  • n = 30 years = 360 months

Substitute the given values into the  Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=779.5353492[/tex]

Therefore, the monthly payments would be $779.54.

Part c)

Given:

  • P = $153,850
  • i = 0.055 per year = 0.055/12 per month
  • n = 30 years = 360 months

Substitute the given values into the Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=873.5433786[/tex]

Therefore, the monthly payments would be $873.54.

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